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30 September, 20:45

g A bank loaned out $17,000, part of it at the rate of 7% per year and the rest at 15% per year. If the interest received in one year totaled $2,000, how much was loaned at 7%

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  1. 30 September, 20:54
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    Amount of Loan @ 7% was $6,875

    Explanation:

    Let

    Amount of Loan @ 7% = X

    Amount of Loan @ 15% = Y

    According to given condition

    X + Y = 17000 (Eq 01)

    X7% + Y15% = 2000

    0.07X + 0.15Y = 2000 (Eq 02)

    By multiplying (Eq 01) with 3

    3X + 3Y = 51,000 (Eq 03)

    By multiplying (Eq 02) with 20

    1.4X + 3Y = 40000 (Eq 04)

    By subtracting (Eq 04) from (Eq 03)

    3X + 3Y - (1.4X + 3Y) = 51,000 - 40,000

    3X + 3Y - 1.4X - 3Y = 11,000

    1.6X = 11,000

    X = 11,000 / 1.6

    X = 6,875

    Placing Value of X in (Eq 01)

    6,875 + Y = 17000

    Y = 17000 - 6,875

    Y = 10,125

    Check:

    0.07 (6,875) + 0.15 (10,125) = 2000

    481.25 + 1,518.75 = 2,000

    2,000 = 2,000

    So

    Amount of Loan @ 7% = X = $6,875
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